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This text explores the surprisingly complex structure of free lattices. The first part of the book presents a complete exposition of the basic theory of free lattices, projective lattices, and lattices which are bounded homomorphic images of a free lattice, as well as applications of these results to other areas. This portion of the book is suitable for use in a graduate course in lattice theory or general algebra. The second part of the book contains new results about free lattices and new proofs of known results, providing the reader with a coherent picture of the fine structure of free lattices. The book closes with an analysis of algorithms for free lattices and finite lattices that is accessible to researchers in other areas and depends only on the first chapter and a small part of the second. Several open problems appear throughout the book and, for easy reference, are assembled in a section at the end. Synthesizing 70 years of research, this is a comprehensive treatment of the theory of free lattices.
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